Finite Group Databasebeta

C16×Dic478 #44486451

order30592
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC16×Dic478

Splittings

SylowC239 ⋊ Q8×C16

Subgroups

subgroupG/H
centerC2×C16C2×D239
commutatorC2×C239C22×C16
FrattiniC2×C8C22×D239
FittingC4×C16×C239C2
socle, prime radicalC22×C239C22×C8
cosocleC2×C8×C239C23
hypercenterC4×C16D239
hypocenterC239Q8×C16
LCSG ▷ C2×C239 ▷ C239
UCSC1 ◁ C2×C16 ◁ C4×C16

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30592

Conjugacy classes & character table

7696 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 6413);